Shatkarmas are six karmas in Tantra that are used for a certain degree of manipulation of the physical realm out of material benefit. During the Old Ages, the fights between the armies extensively used certain aspects of tantric practices to have an edge over the war. Such acts include - hiding certain Yantras or materials (such as stone) that would divide the enemy crews or kill them so as to get an edge over them in the war. One such good example of such Tantric yogi was Chanakya from historical evidence.
Now the methods of shatkarmas would vary from situation to situation, only an experienced yogi is able to construct these certain mantras in that specific situation so that he/she could bring it to full success.
The principle of Tantra, we are concerned with two aspects :- shiva and shakti. The mechanical object into consideration is roughly called shiva and the energy that operates on the mechanical object is usually referred to as shakti. In this route of the philosophy - we seek to control the shakti (or energy aspect that is influenced by the flow of the time) through manipulation of shiva (materialistic aspects using tools like - materials, yantras, mudras, mantras, etc.), Marana is one of them (death).
There are various ways to plan a shatkarmas such as:
1. Yoga
Those proficient in the art of yoga and major and minor siddhis are capable of invoking it to influence the death of people to certain degrees. According to the principles of Advaita - the whole universe (brahman) is composed of self (like a dream is a state of mind), hence the true self is beyond this universe (which is similar to a dream-like state in that sense), and through meditation is capable to get a control like that.
Certain Yogis have the ability to come out of their physical body and influence them, they can use other eternal entities that might be interpreted as ghosts, or spirits by ordinary men for their purpose too.
2. Mantras/Yantras/Tantra
In Tantra, certain body parts are reflections of the parts (or objects) of the Brahman (absolute reality). They use these parts (called Nadis) to get siddhis. The points where Nadis are branched are called Chakras (or flowers as chakras and petals as emerging Nadis from that chakra). Certain Nadis and Chakras are associated with certain siddhis that are easier to get than Yogic methods, for example - Mooldhara Chakra and Ajna Chakras are associated with the siddhis to get the knowledge of past, present, and future, Hrit Chakra (not to be confused with Anahata Chakra!) is associated with the ability to control people emotionally.
Mantras and Yantras are shortcuts to activate them and obtain their siddhis. Mantras are obtained via the extensive practice of Laya Yoga and trial and error. For each given situation, the planning and the mantras might differ. There's no general mantra for all.
Astrological Methods
In astrology, there are materialistic rituals (or sometimes mantras too) that are devoted to shifting astral planets (NOT physical ones!) to change the influence of someone's life. These rituals include using certain stones, gravels, yantras, mantras, etc could also be used to perform shatkarmas in opposite ways.
It is important to note that methods might differ depending on the practice to style of the yogi. They are non-exhaustive. The siddhis, knowledge, and yoga associated with such practices might develop over multiple decades of the time. They should be seen with the intent of distraction. The real purpose of the tools listed above is clear in the Upanishads - to get the knowledge of the infinite cosmos which is liberation.
It is possible that a person who spent years of practices on such practices to NOT be enlightened (jivanmukta) and might not get liberation will surely get bounded by Karmic reactions after such low performances, while the victim who strives liberation might break the laws of karma (jivanmukta) who would get liberated and all of such performances to get nullified for him with absolutely no effect. Thus, striving for enlightenment is always superior to shatkarmas.